The present invention relates to a method for coding a signal sequence of speech or image with a small amount of information and, more particularly, to a multiplexed vector quantization method and apparatus therefor which are robust against transmission channel errors.
A vector quantization method is known as an effective method for coding a signal sequence with a small amount of information. According to this method, discrete values of successive signal samples to be coded are grouped for each predetermined number and defined as a vector for each group, each vector is checked with a codebook containing reconstruction vectors and the index of a reconstruction vector that will minimize a quantization distortion is used as an output code.
FIG. 1 shows the general arrangement for the conventional vector quantization method. Reference numerals 21 and 23 indicate codebooks, 22 an encoder and 24 a decoder. Symbols used herein have the following meanings:
u: input vector
u(i): i-th element of input vector u, where i=0, 1, . . . , k-1
k: vector dimension
r: code transmission rate [bits/sample]
b: transmitting code (kr bits)
Z: codebook
z.sub.l : l-th reconstruction vector contained in codebook Z
z(i,l): i-th element of reconstruction vector z.sub.l
M: number of reconstruction vectors z.sub.l contained in codebook Z, where M=2.sup.kr and l=0, 1, . . . , M-1
d.sub.l : quantization distortion
The codebooks 21 and 23 each have M=2.sup.kr reconstruction vectors z.sub.l, where l=0, 1, . . . , M-1. At the transmitting side, the encoder 22 refers to the codebook 21 for each input vector u, calculates the quantization distortion d.sub.l represented by the square of the distance between each of the M=2.sup.kr reconstruction vectors z.sub.l and the input vector u, determines the reconstruction vector which yields the smalles distortion d.sub.l, and sends its index l as the kr-bit long transmitting code b. The distortion d.sub.l is calculated using the following equation (1): ##EQU1## At the receiving side, the decoder 24 refers to the codebook 23 on the basis of the received transmitting code b (i.e. the reconstruction vector index) and selects and outputs the reconstruction vector corresponding to the received transmitting code b.
This quantization method essentially has the defect of reconstructing a vector entirely different from the input vector when there are channel errors, because the index and the value of the reconstruction vector bear no relationship in terms of distance.
To avoid this, it is necessary in the prior art to suppress the code error rate by use of an error correcting code, that is, by imparting redundancy to the transmitting code. In this instance, the code error rate can significantly be lowered by, for example, using additional redundant bits the amount of which accounts for 50% of the amount of information bits involved. However, this method always requires the same amount of redundant bits even for an error-free channel. That is, where the total amount of information to be transmitted is fixed, the amount of information bits available is only 2/3 of the total amount of information to be sent even if the channel is free from errors, and the quantization distortion will naturally increase. In practice, the code error rate varies with time and it is difficult to modify the channel coding scheme in accordance with the varying error rate, so that it is inevitable to sacrifice the performance either for an error-free channel or for an erroneous channel. Accordingly, the use of error correcting codes is not always effective for reducing the quantization distortion in the case where the amount of information to be sent is fixed. Further, for the distance calculation (i.e. the calculation of the quantization distortion d.sub.l) in the vector quantization by the conventional encoder 22 shown in FIG. 1, the codebook 21 is required to have a storage capacity for storing the M= 2.sup.kr reconstruction vectors z.sub.l, and the distortion d.sub.l must be calculated for each of the M reconstruction vectors. Therefore, the prior art has the disadvantage that the amount of computation and the storage capacity of the codebook each increase as an exponential function of the amount of information kr per vector.